TERRESTRIAL VISITORS

Q&A: The Meaning of Visibility

April 29, 2013

Question: My local weather man reports “visibility” as anything from zero to like 50+ miles. I’ve got a basic idea what that means, but wonder exactly how they come up with that number. I assume he’s talking about a view that’s unobstructed by trees or mountains. I thought Sky Lights might be able to tackle this question. — BT, Minoqua, WI

Answer: That’s a great question BT. Your assumption about “unobstructed views” is correct. Visibility distances are based purely on atmospheric conditions, so if there’s a mountain range in the way, you can’t really see as far as you might.

Here’s the “official” definition of visibility used by the NWS:

During daylight: The greatest distance at which a black object of suitable dimensions (i.e., big enough to see), and situated near the ground, can be seen when observed against a light background.

At Night: The greatest distance at which a light source of 1,000 candela can be seen when observed against a dark background. [You can imagine 1000 candela to be about as bright as a 200 watt incandescent bulb.]

I say “imagine” since there’s no scientific formula to convert candela into watts. The measurement of light intensity gets extremely complex, and depends on things like color, efficiency, and directionality. But for the purpose of this explanation, you can equate 1000 candela to a standard 200 watt light bulb.

Note: Despite those apparently rigorous definitions, the visibility distance will vary between day and night — even under identical atmospheric conditions. The human eye works better during the day. Our night vision is far less efficient.

The image above shows the same scene near Santa Barbara, CA on days with greatly varying visibility. The image didn’t have any specs, but I’d guess the left half shows a visibility of around 40 km (25 miles), and the right half shows a visibility of around 2 km (1.2 miles).

Now we have to do a little math. Seeing an object with human eyes, day or night, requires a minimum contrast ratio of 2% between object and background. Plugging this value into the equation for light extinction in our atmosphere we get:

xv = 3.912/bext

where xv is the visibility distance, and bext is the light extinction coefficient. Lower values of bext represent more clear air; higher values represent conditions like smoke or fog. At sea level on a clear day, bext = 13.2 × 10-6 m-1. That value implies the maximum visibility (xv) is about 250 km (155 miles). The NWS can measure bext using instruments that detect just how clear the air really is.

Visibility of less than 100 meters (330 ft) is usually reported as zero. Under these conditions, roads may be closed, or automatic warning lights and signs may be activated to warn drivers. During an Arizona dust storm, or during a winter snow storm white-out in the Midwest, actual visibility can drop to less than a meter.